Electronic structures of topological quantum materials studied by ARPES

1D topological systems for next-generation electronics

The recently discovered topological quantum materials (TQMs) have electronic structures that can be characterized by certain topological invariants. In these novel materials, the unusual bulk and surface electrons not only give rise to many exotic physical phenomena but also foster potential new technological applications. To characterize the unusual electronic structures of these new materials, investigators have used angle-resolved photoemission spectroscopy (ARPES) as an effective experimental tool to directly visualize the unique bulk and surface electronic structures of TQMs. In this review, we first give a brief introduction of TQMs and ARPES, which is followed by examples of the application of ARPES to different TQMs ranging from topological insulators to Dirac and Weyl semimetals. We conclude with a brief perspective of the current development of ARPES and its potential application in the study of TQMs.

[EN]In three-dimensional topological Insulators, the topological protected helical surface conducting states exist along with the bulk insulating states. In a class of topological insulators, namely topological crystalline insulators, the protection role of surface states is taken by crystalline symmetry instead of time-reversal symmetry. These exotic characteristics bring about potential applications in logic devices, thermoelectricity or quantum computers. However, due to some critical challenges (like their compatibility with the existing devices, their fabrication processes as well as their compatibility with topological or quantum behavior under external stimuli, working temperature range, cost efficiency, practical structure and ease of use), topological materials are still lagging in device applications. In this regard, this thesis aims at investigating the fundamental properties of a topological crystalline insulator, 𝑃𝑏0.77𝑆𝑛0.23𝑆𝑒, based on Raman characterization at different temperature ranges and low magnetic fields as well as magneto-transport of its Hall bar devices at low temperatures, albeit with meeting challenges in fabrication and characterization. The Raman response of this material at relaxed conditions confirms the presence of topological surface states. Moreover, temperature-dependent Raman characterizations indicate that both surface states and their bulk counterparts contribute to the Raman response considering the interplay of electrons and phonons. Furthermore, our findings based on magnetic-field dependent Raman characterization demonstrate that the surface states are topologically protected by symmetry. These Raman results are also corroborated with magneto-transport characterizations, revealing the prominent role of an inherent attribute of this material based on strong spin-orbit coupling. Our results pave the way for electron studies in field-effect transistors based on topological phase transitions

In this review, we discuss recent progress in the explorations of topological materials beyond topological insulators; specifically, we focus on topological crystalline insulators and bulk topological superconductors. The basic concepts, model Hamiltonians, and novel electronic properties of these new topological materials are explained. The key role of the symmetries that underlie their topological properties is elucidated. Key issues in their materials realizations are also discussed.

Topological insulators represent unusual topological quantum states, typically with gapped bulk band structure but gapless surface Dirac fermions protected by time-reversal symmetry. Recently, a distinct kind of topological insulator resulting from nonsymmorphic crystalline symmetry was proposed in the KHgX ($X=\mathrm{As}$, Sb, Bi) compounds. Unlike regular topological crystalline insulators, the nonsymmorphic glide-reflection symmetry in KHgX guarantees the appearance of an exotic surface fermion with hourglass shape dispersion (where two pairs of branches switch their partners) residing on its (010) side surface, contrasting to the usual two-dimensional Dirac fermion form. Here, by using high-resolution angle-resolved photoemission spectroscopy, we systematically investigate the electronic structures of KHgSb on both (001) and (010) surfaces and reveal the unique in-gap surface states on the (010) surface with delicate dispersion consistent with the ``hourglass Fermion'' recently proposed. Our experiment strongly supports that KHgSb is a nonsymmorphic topological crystalline insulator with hourglass fermions, which serves as an important step to the discovery of unique topological quantum materials and exotic fermions protected by nonsymmorphic crystalline symmetry.

Bismuth is gaining importance as a key element of functional quantum materials. The effects of spin-orbit coupling (SOC) are at the heart of many exciting proposals for next-generation quantum technologies, including topological materials for efficient information transmission and energy-saving applications. The "heavy" element bismuth and its compounds are predestined for SOC-induced topological properties, but materials design is challenged by a complex link between them and the chemical composition and crystal structure. Nevertheless, a lot can be learned about a certain property by testing its limits with compositional and/or structure modifications. We survey a handful of topological bismuth-based materials that bear structural and chemical semblance to the early topological insulators, antimony-doped elemental bismuth, Bi2Se3 and Bi2Te3. Chemical bonding via p orbitals and modular structure underlie all considered bismuth chalcogenides, subhalides, and chalcogenide halides and allow us to correlate the evolution of chemical bonding and structure with variability of the topological properties, although materials design should not be regarded as a building blocks set. Over the past decade, material discoveries have unearthed a plethora of topological properties, and bismuth is very fertile as a progenitor of a rich palette of exotic quantum materials, ranging from strong and weak 3D and crystalline topological insulators over topological metals and semimetals to magnetic topological insulators, while preserving the general layered structure motif.

Topological materials in crystal solids, including topological insulators (TIs), topological crystalline insulators (TCIs), topological Dirac semimetals (DSMs), topological Weyl semimetals (WSMs), topological Dirac or Weyl nodal line semimetals (NLSMs) and beyond, are mainly featured with topological, protected non-trivial surface states, and their bulk phases are insulators or semimetals with the proper presence of Dirac cones, Weyl nodes or Dirac nodal lines around the Fermi level. The author suggests a two-step computational screening strategy of 3D topological materials by mixing chemistry with physics with the considerations of fully filled bands and band inversion.

The properties that distinguish topological crystalline insulator (TCI) and topological insulator (TI) rely on crystalline symmetry and time-reversal symmetry, respectively, which encodes different bulk and surface/edge properties. Here, we predict theoretically that electron-doped TlM (M = S and Se) (110) monolayers realize a family of two-dimensional (2D) TCIs characterized by mirror Chern number CM = -2. Remarkably, under uniaxial strain (≈ 1%), a topological phase transition between 2D TCI and 2D TI is revealed with the calculated spin Chern number CS = -1 for the 2D TI. Using spin-resolved edge states analysis, we show different edge-state behaviors, especially at the time reversal invariant points. Finally, a TlBiSe2/NaCl quantum well is proposed to realize an undoped 2D TCI with inverted gap as large as 0.37 eV, indicating the high possibility for room-temperature observation.

Superconductors derived from topological insulators and topological crystalline insulators by doping have long been considered to be candidates as topological superconductors. Pb$_{0.5}$Sn$_{0.5}$Te is a topological crystalline insulator with mirror symmetry protected surface states on (001), (011) and (111) oriented surfaces. The superconductor (Pb$_{0.5}$Sn$_{0.5}$)$_{0.7}$In$_{0.3}$Te is induced by In doping in Pb$_{0.5}$Sn$_{0.5}$Te, and is thought to be a topological superconductor. Here we report the first scanning tunneling spectroscopy measurement of the superconducting state as well as the superconducting energy gap in (Pb$_{0.5}$Sn$_{0.5}$)$_{0.7}$In$_{0.3}$Te on a (001)-oriented surface. The spectrum can be well fitted by an anisotropic $s$-wave gap function of $\Delta=0.72+0.18\cos4\theta$ meV using Dynes model. The results show that the quasi-particle density of states seem to be fully gapped without any in-gap states, in contradiction with the expectation of a topological superconductor.

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to the combination of spin-orbit interactions and time-reversal symmetry. The two-dimensional (2D) topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A three-dimensional (3D) topological insulator supports novel spin-polarized 2D Dirac fermions on its surface. In this Colloquium the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topological insulators have been observed. Transport experiments on $\mathrm{Hg}\mathrm{Te}∕\mathrm{Cd}\mathrm{Te}$ quantum wells are described that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. Experiments on ${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$, ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$, and ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$ are then discussed that establish these materials as 3D topological insulators and directly probe the topology of their surface states. Exotic states are described that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions and may provide a new venue for realizing proposals for topological quantum computation. Prospects for observing these exotic states are also discussed, as well as other potential device applications of topological insulators.

This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topological indices. The book also analyzes recent topics in condensed matter theory and concludes by surveying active subfields of research such as insulators with point-group symmetries and the stability of topological semimetals. Problems at the end of each chapter offer opportunities to test knowledge and engage with frontier research issues. Topological Insulators and Topological Superconductors will provide graduate students and researchers with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field.

Recently a series of new topological materials, such as topological insulator, topological semimetal, topological superconductor have been discovered through a large number of magneto-transport measurements in high magnetic field, which greatly promotes the research process of topological quantum materials. The physical properties such as SdH oscillations can be observed from accurately measuring the magnetoresistance effect. The experimental environment puts higher requirements for data acquisition and processing procedures in topological materials measurements for the characteristics of high noise and short discharge time in pulsed high magnetic field. However, the references rarely mentions the related solutions. In this paper, a complete set of detection methods and data processing strategies for topological materials in pulsed high magnetic field environment are proposed. Here we introduce a digital lock-in amplifier and optimize the parameters of FIR filters. Based on NI-PXI-5105 and Labview, the model of fast auto-detection digital lock-in system is carried out. Taking the WTe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> sample to experiment, the magneto-resistance detection and data analysis were performed in 65T pulsed magnetic field. A clear magnetoresistance curve with the significant SdH quantum oscillation at different temperatures was obtained. The results proved that this method is effective and applicable to complete the measurement technology of topological quantum materials in high magnetic field.

Angle-resolved photoemission spectroscopy (ARPES) is a widely used characterization technique in condensed matter physics, providing direct access to the single-electron spectral function of crystals, including their electronic band structure and Fermi surface. Measuring the band structure of novel quantum materials has been fundamentally important for determining, for example, nontrivial band topology, as in topological insulators, Weyl semimetals, and Dirac semimetals, or for identifying new classes of materials, such as altermagnets. A key challenge with these emerging quantum materials is that their initial crystalline quality is rarely optimized, which directly affects the spectra measured by ARPES. Here, we present a theoretical framework and experimental evidence addressing two common consequences of static disorder in photoemission experiments: the loss of coherent spectral weight and the broadening of spectral features. ARPES spectra can be understood as a sum of coherent and incoherent intensities, with their relative contributions controlled by atomic disorder and electron correlation effects. For disorder caused by phonons, the coherent intensity is exponentially suppressed as temperature increases, a phenomenon analogous to the Debye-Waller factor in diffraction, where Bragg peaks diminish in favor of diffuse scattering as disorder increases. In this work, we report a soft-x-ray study of the deliberately disordered (via Ar ion sputtering) InAs(110) surface, characterized by scanning tunneling microscopy, scanning tunneling spectroscopy, and low-energy electron diffraction. We introduce a framework that enables quantification of coherent photoemission intensity loss with increasing disorder, allowing both thermal and static disorder to be treated within a unified approach. Additionally, we identify a second major effect of disorder beyond lifetime broadening: inhomogeneous spectral broadening arising from local potential fluctuations. We show that such fluctuations increase the linewidths of the spectra of localized and delocalized states and contribute to the suppression of ARPES intensity from states near the Fermi level. The concepts and analysis methods presented should make ARPES useful for direct diagnosis of disorder effects on electronic states, for science as well as engineering.

We predict planar Sb/Bi honeycomb to harbor a two-dimensional (2D) topological crystalline insulator (TCI) phase based on first-principles computations. Although buckled Sb and Bi honeycombs support 2D topological insulator (TI) phases, their structure becomes planar under tensile strain. The planar Sb/Bi honeycomb structure restores the mirror symmetry, and is shown to exhibit non-zero mirror Chern numbers, indicating that the system can host topologically protected edge states. Our computations show that the electronic spectrum of a planar Sb/Bi nanoribbon with armchair or zigzag edges contains two Dirac cones within the band gap and an even number of edge bands crossing the Fermi level. Lattice constant of the planar Sb honeycomb is found to nearly match that of hexagonal-BN. The Sb nanoribbon on hexagonal-BN exhibits gapped edge states, which we show to be tunable by an out-of-the-plane electric field, providing controllable gating of edge state important for device applications.

Topological materials with exotic quantum properties are promising candidates for quantum spin electronics. Different classes of topological materials, including Weyl semimetal, topological superconductor, topological insulator and Axion insulator, etc., can be connected to each other via quantum phase transition. For example, it is believed that a trivial band insulator can be twisted into topological phase by increasing spin-orbital coupling or changing the parameters of crystal lattice. With the results of LDA calculation and measurement by angle-resolved photoemission spectroscopy (ARPES), we demonstrate in this work that the electronic structure of SrSn2As2 single crystal has the texture of band inversion near the critical point. The results indicate the possibility of realizing topological quantum phase transition in SrSn2As2 single crystal and obtaining different exotic quantum states.